Image texture not showing on object
You probably didn't add a uvmap. A UV map is what maps the 3d coordinates of the object to the 2d coordinates of the Image being used as a texture.

 

Notice properties -> Data -> UV Maps has no entries.

The simplest way to see a texture there is to press the + symbol to the right. Your viewport rendering will show a texture on the Cube.

See blender's manual page about uv_mapping.